In History & Mathematics: Trends and Cycles. Volgograd,Russia: Uchitel Publishing House. pp. 9-48 (2014)

Authors
Leonid Grinin
National Research University Higher School of Economics
Abstract
In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically.
Keywords social evolution  biological evolution  mathematical model  population growth  hyperbolic growth
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Towards a Unified Science of Cultural Evolution.Alex Mesoudi, Andrew Whiten & Kevin N. Laland - 2006 - Behavioral and Brain Sciences 29 (4):329-347.
Macrohistory and Globalization.Leonid Grinin - 2012 - Uchitel Publishing House.
Secular Cycles.Peter Turchin & Sergey A. Nefedov - 2009 - Princeton University Press.

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